Manifold-valued maps occur in material sciences (liquid crystals, superconductivity), physics (gauge theories) and mathematics (harmonic maps). The Winter School "Nonlinear Function Spaces in Mathematics and Physical Sciences" consists of five lectures delivered by leading experts, intended to Master and PhD students, as well as to researchers. The program goes from an introductory course on the basic tools in the study of nonlinear function spaces to very recent results on weak density problems. The school is intended to give junior participants a significant overview of the relevant problems, answers and tools, and all participants the opportunity to discuss the perspectives of the field. Afternoon is in part left to free discussions and open problems sessions.

Lectures:

John Ball (Oxford)
Function spaces for liquid crystals

Fabrice Bethuel (Paris 6)
From singularities for Sobolev spaces into manifolds to branched transportation

Robert Hardt (Rice)
Spaces of Flat and Normal Chains and Cochains

Augusto Ponce (Louvain)
Sobolev spaces into manifolds: a toolbox

Tristan Rivière (ETH Zürich)
The variations of Yang-Mills Lagrangian